Will Blender charge me for exporting videos?
No, Blender will not charge you.

Blender is an open source 3D development software that provides free access for anyone to do almost anything they want with it.

Even if it was, you will find that many programs will provide free student copies and accessibilities.

Taken from the licence page:


  This license grants people a number of freedoms:
  
  
  You are free to use Blender, for any purpose
  You are free to distribute Blender
  You can study how Blender works and change it
  You can distribute changed versions of Blender
  


The Majority of restrictions are for the source code and software distribution.

As @Duarte Farrajota Ramos said, you should take a look at the licence if you have any queries.

Good luck with your project and I hope I helped,

BFB